Name
Period ____
GP
GEOMETRIC PROOFS
1) I can define, identify and illustrate the following terms
Conjecture
Conclusion
Theorem
Inductive
Proof
Prove
Deductive
Postulate
Given
Negation
Counterexample
Dates, assignments, and quizzes subject to change without advance notice.
Monday
Tuesday
Block Day
Friday
3/4
Assumptions &
Justifications; Making
Conclusions
8
9
STUDENT HOLIDAY
Writing Proofs
Fill in the Blank Proofs
10/11
Practice Quiz
Review
5
Fill in the Blank and
Plan Proofs
12
TEST 4
Wednesday, 10/3 and Thursday, 10/4
Assumptions and Justifications
Making conclusions
I can make correct assumptions from a picture, words, or statement.
I can justify a conclusion with a definition, theorem, or postulate.
I can make and justify the next logical conclusion from a given statement.
ASSIGNMENT: Assumptions, Justifications, and Conclusions Worksheet, Completed:
pg. 113-114 (4, 7, 8)
Friday, 10/5
Fill in the Blank and Plan Proofs
I can write a two column proof given a plan.
ASSIGNMENT: : pg. 113-114 (4, 7, 8) and Proofs Worksheet #1
Completed:
Tuesday, 10/9
Writing Proofs
I can write a two column proof.
ASSIGNMENT: Proofs Worksheet #2
Completed:
Wednesday, 10/10 and Thursday, 10/11
Review
*I can review for the test in class.
ASSIGNMENT: Review WS
Completed:
Friday, 10/12
Test 3 – Logic and Proofs
I can demonstrate knowledge skills, and reasoning ability of ALL previously learned material.
ASSIGNMENT: Test #3
Grade:
Assumptions and Justifications
Use page 73 in your book to help complete the notes below…
Things You Can Assume From a Diagram
Things You CAN’T Assume From a Diagram
I. For each picture list the facts you can assume from it.
C
A
T
M
L
W
P
N
H
1
U
Q
R
1
X
U
Y
L
M
2
3
N
II. Based on the picture alone, determine if each statement is true or false.
1. ET SR
5. MO ≅ OE
M
2. MES is a right angle.
6. OET ≅ TES
O
3. T is between E and H.
7. O and R are collinear.
4. M, O, S, and H are coplanar.
8
8. MTH is a right angle.
H
T
R
E
S
1. AEB is an acute angle. 6. BEC and ECB are supplementary.
A
B
E
C
D
2. AE BC
7. AEB and BEC are complementary.
3. AB ⊥ BC
8. C is the midpoint of BD .
4. AB < AE
9. BCE and ECD are a linear pair.
5. mECB = 90°
10. ABE and EBC are complementary.
III. For each statement and its next logical conclusion, tell which definition, postulate, or theorem gives the justification.
1. Given: AM ≅ WU
Conclusion: AM = WU
11. Given:
Why: _________________________________
Conclusion: U is the midpoint of RN
2. Given: E is the midpoint of BD
Conclusion: BE ≅ ED
Why: _________________________________
Why: _________________________________
3. Given: A bisects CT
Conclusion: CA ≅ AT
R
N
8
9
12. Given:
Conclusion: 8 and 9 are vertical
Why: _________________________________
Why: _________________________________
4. Given: CO = OL
Conclusion: CO ≅ OL
13. Given: mNAT + mWED = 90°
Conclusion: NAT & WED are complementary
Why: _________________________________
Why: _________________________________
5. Given: DAY and YAK are a linear pair.
Conclusion: DAY & YAK are supplementary
14. Given: FA ≅ RM
Conclusion: FA = RM
Why: _________________________________
Why: _________________________________
6. Given: TOM is the supplement of SUE
Conclusion: mTOM + mSUE = 180°
Why: _________________________________
7. Given: A and B lie in Plane JOG
Conclusion: A and B are collinear
Why: _________________________________
15. Given: MA = TH
Conclusion: MA ≅ TH
Why: _________________________________
16. Given: mAFD + mBAT = 180°
Conclusion: AFD & BAT are supplementary
Why: _________________________________
F
8. Given: A is in the interior of GLD
Conclusion: mGLA + mALD = mGLD
R
O
G
Why: _________________________________
17. Given:
9. Given: 1 is the complement to 3
Conclusion: m1 + m3 = 90°
Conclusion: FRO ≅ ORG
Why: _________________________________
10. Given: HAM is vertical to EAT
Conclusion: HAM ≅ EAT
Why: _________________________________
Why: _________________________________
18. Given: m 2 = m6
Conclusion: 2 ≅ 6
Why: _________________________________
Name: ___________________________________
Period:_____
Making Conclusions
1. Given: TO ≅ AN
M
Conclusion:
I
8. Given:
K
7
5
E
Justification:
Conclusion:
2. Given: E is the midpoint of BD
Justification:
Conclusion:
9. Given: E
Justification:
F
G
Conclusion:
3. Given: A bisects CT
Justification:
Conclusion:
Justification:
F
4. Given: CO = OL
E
Conclusion:
Justification:
Justification:
5. Given: DAY and YAK are a linear pair
Conclusion:
Justification:
6. Given: TOM is the supplement of SUE
Conclusion:
Justification:
T
Conclusion:
Justification:
12. Given: CAT and RAP are vertical angles.
Conclusion:
Justification:
Given:
11. Given: mABC = mHIJ
Conclusion:
Justification:
7.
G
10. Given:
Conclusion:
M
D
6 5
U
S
13. Given: SAT ≅ ACT
Conclusion:
Justification:
14. Given: A is in the interior of GLD
Conclusion:
Justification:
15. Given: FA ≅ RM
8
9
Conclusion:
21. Given:
Justification:
Conclusion:
16. Given: HAM is vertical to EAT
Justification:
Conclusion:
M
Justification:
I
L
K
22. Given:
R
U
N
17. Given:
Conclusion:
Justification:
Conclusion:
Justification:
23. Given: PAI and IAR are a linear pair
8
9
18. Given;
Conclusion:
Justification:
19. Given: mNAT + mWED = 90°
Conclusion:
Justification:
Conclusion:
Justification:
24. Given: CAT and RAP are complementary
angles.
Conclusion:
Justification:
25. Given: mNAT + mWED = 180°
Conclusion:
20. Given: UB bisects RUY
Justification:
Conclusion:
Justification:
26. Given: A is between J and M
Conclusion:
Justification:
“Making Conclusions” Worksheet continues on the next page…
For #27 and 28, a two column proof is given but steps are missing. Fill in the missing steps and
rewrite the whole proof correctly.
27.
1
3 4
2
Given: 1 is supplementary to 2, 3 is supplementary
to 4, and 2 ≅ 4
Prove: 1 ≅ 3
Statements
Reasons
1.
1 & 2 are supp.
3 & 4 are supp.
Given
2.
m1 + m 2 = 180°
m3 + m 4 = 180°
Def. of Supplement.
3.
m1 + m 2 = m 3 + m 4
Transitive Prop.
6.
m1 + m 4 = m 3 + m 4
Substitution prop,
Steps __ and __
7.
m1 ≅ m3
Subtraction prop.
8.
1 ≅ 3
Def. of ≅
4.
5.
M
K
7
5 E
I
Given: 5 is complementary to 7
28.
Prove: MI ⊥ IE
Statements
Reasons
1.
5 & 7 are comp.
Given
2.
m5 + m 7 = 90°
Def. of complement.
4.
mMIE = 90°
Substitution, steps __ and __
6.
MI ⊥ IE
Definition of perpendicular
3.
P 113 (4, 7, 8)
Name:
Period:
Proofs Worksheet #1
On a separate paper, write a two-column proof for each problem 1-5. Follow the plan provided for help.
1. Given: RT ≅ SU
Prove: RS = TU
R
S
T
U
Plan: Use the definition of congruent segments to write the given information in terms of lengths. Next
use the Segment Addition Postulate to write RT in terms of RS + ST and SU as ST + TU. Substitute
those into the given information and use the Subtraction Property of Equality to eliminate ST and leave
RS = TU.
2. Given: m5 = 47°
Prove: m 6 = 133°
T
M
6 5
U
S
Plan: Use the Linear Pair Theorem to show that 5 and 6 are supplementary. Then use the
definition of supplementary angles to show that their measures add up to 180°. Finally use substitution
and then subtraction to arrive at the “Prove” statement.
3. Given: AB = BC
BC = BD
Prove: B is the midpoint of AD
A
D
B
C
Plan: Write the “Given” information and use the transitive property to show that AB=BD. Then use
the definition of congruence to show that the segments are congruent and the definition of midpoint to
finish the proof.
4. Given: l bisects MN at P
Prove: MP = PN
M
P
N
l
Plan: Use the definition of bisect to show the two smaller segments are congruent. Then use the
definition of congruence to show that their lengths are equal.
5. Given: 1 and 2 are supplementary;
1 ≅ 3
Prove: 3 and 2 are supplementary
1
2
3
Plan: Use the definition of supplementary angles and congruent angles to write the given information
in terms of angle measures. Next use substitution to show that m3 + m 2 = 180° . Then use the
definition of supplementary angles for the conclusion.
Proofs Worksheet #2
W
N
1.
M
O
Given: O is the midpoint of MN
OM = OW
Prove: OW = ON
W
1 2
U
3.
X
O
X
Q
R
L
M
N
B
C
C
12
D
3
F
E
D
1 2
Given: 1 ≅ 2
Prove: 1 and 2 are right angles
W
1 2
U
Y
Given: m1 = 90°
Prove: m 2 + 90 = 180
8.
Given: AB ≅ CD
Prove: AC ≅ BD
11.
B
A
6.
J K
L
1 2
3 M
P
A
D
C
E
Given: 1 and 2 are complementary
3 and 2 are complementary
Prove: m1 = m3
Given: PR ≅ LN
Q is the midpoint of PR
M is the midpoint of LN
Prove: PQ = LM
9.
B
Y
Given: m1 = m3
Prove: mJOL = mKOM
7.
A
Given: AB = CD
Prove: AC = BD
4.
Given: m1 = 90°
Prove: m 2 = 90°
5.
2.
D
G
Given: EF ⊥ EG
D is in the interior of FEG
Prove: FED and DEG are complementary
10.
1
2
Given: 1 and 2 are supplementary
1 ≅ 2
Prove: 1 and 2 are right angles
2
1
12.
3
Given: 1 and 2 are complementary
Prove: 2 and 3 are complementary
13.
14.
2
1
A
Given: AD bisects BAC
12
1 ≅ 3
3
Prove: 2 ≅ 3
B
D
Given: m 2 = 2(m1)
Prove: m1 = 60°
15.
1
2
C
16.
E
F
G
C
D
C
B
A
Given: ABC is a right angle
Prove: 1 and 2 are complementary
Given: CD ≅ EF
CD ≅ FG
Prove: F is the midpoint of EG
A
17.
K
H
U
F
Given: KU = HF
Prove: KH ≅ UF
A
19.
B
18.
1
B 2
Given: mABC = mCBD
Prove: BC is the angle bisector of ABD
3
4
D
Given: ABD and CDB are right angles
m 2 = m 4
Prove: m1 = m3
C
D
C
F
20.
C
E
B
D
A
Given: mABE = mCBE
Prove: ABD and DBE are complementary